Your Great Great Grandmother was not full blooded Cherokee. She is in the American census as born in Indiana and her entire family is listed as white. That's why it doesn't show up in a DNA test. Now, it is possible that if you went back several generations there was some Native ancestry and it has filtered out in time, but more likely you don't have any Native ancestry. So many people have stories like yours that are handed down and they are usually apocryphal.